The Golden R atio. By Rachel Lewis. adapted from http://www.geom.uiuc.edu/~demo5337/s97b/discover.htm. Goal. Students will calculate the Golden Ratio and discover where it exists in the world around them.
By Rachel Lewis
adapted from http://www.geom.uiuc.edu/~demo5337/s97b/discover.htm
Students will calculate the Golden Ratio and discover where it exists in the world around them.
From this picture, students are asked to measure the length and width of their favorite rectangle in centimeters and to record these values in the table in their packets.
Students are then told to walk around the classroom and find various rectangles to measure. All data is to be recorded in the same table.
Students are then asked to calculate the ratio of length to width for each rectangle the measure using the formula:
*These values should be the same for each student
The number you have calculated should be close to 1.61803. This is called the Golden Ratio. Remember the Fibonnaci sequence we studied before? Well you will notice that if we find the ratio of consecutive numbers…
2/1 = 2.0 3/2 = 1.5 5/3 = 1.67
8/5 = 1.6 13/8 = 1.625 21/13 = 1.615
34/21 = 1.619 55/34 = 1.618 89/55 = 1.618
the result gets closer and closer to the Golden Ratio! The number first got its fame in Ancient Greece when mathematicians noticed how frequently it appeared in geometry. This ratio is said to be used in architecture from the Parthenon in Greece to the Great Mosque of Kairoun in Tunisia. Leonardo DaVinci’s famous drawing to the left shows a man drawn within a pentagon, suggests that the Golden Ratio exists in the human form.